Finite Element Modeling of Nanoindentation Measurements of Crystalline and Amorphous Si
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Finite Element Modeling of Nanoindentation Measurements of Crystalline and Amorphous Si J. A. Knapp, D. M. Follstaedt, S. M. Myers, and G. A. Petersen Sandia National Laboratories, Albuquerque, NM 87185-1056 ABSTRACT Nanoindentation testing of amorphous Si layers, formed by self-ion implantation, has been performed, and their mechanical properties compared to crystalline Si. The data was analyzed using finite element modeling of the indentation measurement, allowing the properties of the thin amorphous layers to be separated from those of the underlying material. By modeling the materials as isotropic, elastic-plastic solids with the Mises yield criterion, the amorphous Si is shown to have a hardness about 15% lower than crystalline Si and an elastic modulus about 10% lower. Electron and atomic force microscopies of the indents indicate that the amorphous Si does not undergo phase changes during indentation, and that it may be somewhat more ductile than crystalline Si. INTRODUCTION Finite-element modeling (FEM) has proven to be a valuable tool for interpreting nanoindentation measurements obtained from samples such as thin films or ion-implanted layers, allowing the mechanical properties of the films to be separated from those of the underlying substrates. For the case of Si, the measurement is greatly complicated by pressure-induced phase changes and cracking around deep indents.[1-3] We have performed extensive indentation testing of both crystalline and self-ion-implanted, amorphous Si, on both bulk Si and Si-on-Insulator (SOI) substrates. The residual indents were examined with atomic force microscopy (AFM) and both secondary (SEM) and transmission electron microscopy (TEM). Detailed finite-element simulations[4] of the indentations were performed with the usual 2-dimensional axisymmetric approximation in order to quantify and compare mechanical properties, as well as with a full 3dimensional description in selected cases. Although the elastic properties of amorphous Si have been measured by another technique[5], plastic properties have not been reported previously. INDENTATION AND MICROSCOPY Two types of Si samples were used: bulk crystalline Si wafers, with (100), (110), and (111) orientations, and SOI samples, with (100) and (111) orientations. To form amorphous Si (a-Si) layers, each sample was implanted with Si ions at 300 keV to 3.0x1015 Si/cm2 and at 100 keV to 3.0x1015 Si/cm2 . This treatment, resulting in 1-2 Si displacements/atom at room temperature, gives an amorphous layer ~600 nm thick on bulk, crystalline Si. For the SOI samples, the Si overlayer was only 415 nm thick, so the entire layer was amorphized, with a 1 µm thick oxide layer underneath. Atomic force microscopy (AFM) measurements show a 12 nm step at the edge of the implanted area, allowing us to calculate a density reduction relative to crystalline Si of -2.0 %, consistent with observations by others.[5,6] By comparing mechanical results from several orientations of the implanted Si, any residual orientation effects in the amorphous Q1.2.1
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